Subgroups — C₈₉×#21550 #36399398

Order 22784.

914 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3054	C₂	1	1	yes	maximal, characteristic
2	C₂×#444×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2929	C₂	1	2	yes	maximal, complemented
4	C₂×#405×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#1974	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#1945	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1937	C₂	1	2	yes	maximal, complemented
8	C₈₉×#1897	C₂	1	2	yes	maximal, complemented
9	C₈₉×#1811	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1773	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1765	C₂	1	2	yes	maximal, complemented
12	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
13	C₂×#131×C₈₉	C₂²	1	2	yes	—
14	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
16	#525×C₈₉	C₂²	1	2	yes	—
17	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
18	#470×C₈₉	C₄	1	2	yes	complemented
19	#469×C₈₉	C₄	1	2	yes	complemented
20	#468×C₈₉	C₄	1	4	yes	complemented
21	#444×C₈₉	—	2	4	no	—
22	#435×C₈₉	—	2	4	no	—
23	C₈×D₄×C₈₉	—	2	4	no	—
24	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
26	#427×C₈₉	C₂²	1	1	yes	characteristic
27	#424×C₈₉	C₂²	1	2	yes	—
28	C₂×#104×C₈₉	C₂²	1	2	yes	—
29	C₂×#104×C₈₉	C₂²	1	2	yes	—
30	#416×C₈₉	C₂²	1	2	yes	—
31	#408×C₈₉	C₂²	1	2	yes	—
32	#407×C₈₉	C₂²	1	2	yes	—
33	#405×C₈₉	—	2	4	no	—
34	#405×C₈₉	C₂²	1	2	yes	—
35	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
39	#341×C₈₉	C₂²	1	2	yes	—
40	#339×C₈₉	C₂²	1	2	yes	—
41	#339×C₈₉	C₂²	1	2	yes	—
42	C₂×#41×C₈₉	C₂³	1	2	yes	—
43	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
44	#135×C₈₉	—	2	2	no	—
45	#135×C₈₉	—	2	2	no	—
46	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
47	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	—
48	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic
49	#131×C₈₉	—	2	4	no	—
50	#131×C₈₉	—	2	4	no	—
51	C₂×M₁₆×C₈₉	—	2	2	no	—
52	C₂×M₁₆×C₈₉	—	2	2	no	—
53	C₂×M₁₆×C₈₉	—	2	2	no	—
54	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
55	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
56	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
57	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
58	C₂²×C₈×C₈₉	—	2	2	no	—
59	C₂²×C₈×C₈₉	—	2	2	no	—
60	C₂²×C₈×C₈₉	—	2	2	no	—
61	C₂²×C₈×C₈₉	D₄	1	4	yes	—
62	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
66	#123×C₈₉	—	2	2	no	—
67	C₂²⋊Q₈×C₈₉	C₂×C₄	1	4	yes	—
68	#121×C₈₉	C₂×C₄	1	4	yes	—
69	#120×C₈₉	—	2	2	no	—
70	C₄×D₄×C₈₉	—	2	4	no	—
71	#117×C₈₉	—	2	2	no	—
72	#117×C₈₉	—	2	2	no	—
73	#117×C₈₉	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
76	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
78	#108×C₈₉	—	2	2	no	—
79	#108×C₈₉	—	2	2	no	—
80	#107×C₈₉	C₂×C₄	1	2	yes	—
81	#106×C₈₉	C₂×C₄	1	2	yes	—
82	C₄⋊C₈×C₈₉	—	2	4	no	—
83	#104×C₈₉	—	2	4	no	—
84	#104×C₈₉	—	2	4	no	—
85	#103×C₈₉	C₂×C₄	1	4	yes	—
86	#102×C₈₉	C₂×C₄	1	4	yes	—
87	C₂²⋊C₈×C₈₉	—	2	4	no	—
88	C₂²⋊C₈×C₈₉	—	2	4	no	—
89	#97×C₈₉	—	2	2	no	—
90	#97×C₈₉	—	2	2	no	—
91	#97×C₈₉	D₄	1	4	yes	complemented
92	C₄×C₈×C₈₉	—	2	2	no	—
93	C₄×C₈×C₈₉	—	2	2	no	—
94	C₄×C₈×C₈₉	—	2	2	no	—
95	C₂⁴×C₈₉	#41	1	1	yes	characteristic
96	#41×C₈₉	—	2	2	no	—
97	#41×C₈₉	—	2	2	no	—
98	#41×C₈₉	—	2	2	no	—
99	#41×C₈₉	—	2	2	no	—
100	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
101	C₂×D₄×C₈₉	—	2	4	no	—
102	C₂×D₄×C₈₉	—	2	2	no	—
103	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₈₉	—	2	1	no	—
105	C₂²×C₄×C₈₉	—	2	1	no	—
106	C₂²×C₄×C₈₉	—	2	1	no	—
107	C₂²×C₄×C₈₉	—	2	1	no	—
108	C₂²×C₄×C₈₉	—	2	1	no	—
109	C₂²×C₄×C₈₉	—	2	1	no	—
110	C₂²×C₄×C₈₉	—	2	2	no	—
111	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
114	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
115	Q₁₆×C₈₉	—	2	2	no	—
116	SD₁₆×C₈₉	—	2	4	no	—
117	D₈×C₈₉	—	2	2	no	—
118	M₁₆×C₈₉	—	2	4	no	—
119	M₁₆×C₈₉	—	2	4	no	—
120	M₁₆×C₈₉	—	2	2	no	—
121	M₁₆×C₈₉	—	2	2	no	—
122	M₁₆×C₈₉	—	2	2	no	—
123	M₁₆×C₈₉	—	2	2	no	—
124	M₁₆×C₈₉	—	4	4	no	—
125	C₂×C₈×C₈₉	—	2	1	no	—
126	C₂×C₈×C₈₉	—	2	1	no	—
127	C₂×C₈×C₈₉	—	2	1	no	—
128	C₂×C₈×C₈₉	—	2	1	no	—
129	C₂×C₈×C₈₉	—	2	8	no	—
130	C₂×C₈×C₈₉	—	2	2	no	—
131	C₂×C₈×C₈₉	—	2	2	no	—
132	C₂×C₈×C₈₉	—	4	4	no	—
133	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
138	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₈₉	#41	1	2	yes	—
141	C₂×C₈×C₈₉	#41	1	2	yes	—
142	C₄⋊C₄×C₈₉	—	2	4	no	—
143	C₄⋊C₄×C₈₉	—	2	4	no	—
144	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
145	C₂²⋊C₄×C₈₉	—	2	4	no	—
146	C₂²⋊C₄×C₈₉	—	2	4	no	—
147	C₂²⋊C₄×C₈₉	—	2	2	no	—
148	C₂²⋊C₄×C₈₉	—	2	4	no	—
149	C₄²×C₈₉	—	2	1	no	—
150	C₄²×C₈₉	—	2	2	no	—
151	C₄²×C₈₉	—	2	1	no	—
152	C₄²×C₈₉	C₂×D₄	1	2	yes	—
153	C₄²×C₈₉	#41	1	2	yes	—
154	C₂³×C₈₉	—	2	1	no	—
155	C₂³×C₈₉	—	2	1	no	—
156	C₂³×C₈₉	—	2	2	no	—
157	C₂³×C₈₉	—	4	2	no	—
158	C₂³×C₈₉	C₄×D₄	1	2	yes	—
159	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
160	Q₈×C₈₉	—	2	2	no	—
161	Q₈×C₈₉	—	2	2	no	—
162	D₄×C₈₉	—	2	2	no	—
163	D₄×C₈₉	—	2	2	no	—
164	D₄×C₈₉	—	4	8	no	—
165	D₄×C₈₉	—	4	2	no	—
166	D₄×C₈₉	—	4	2	no	—
167	C₂×C₄×C₈₉	—	2	1	no	—
168	C₂×C₄×C₈₉	—	2	1	no	—
169	C₂×C₄×C₈₉	—	2	2	no	—
170	C₂×C₄×C₈₉	—	2	2	no	—
171	C₂×C₄×C₈₉	—	2	2	no	—
172	C₂×C₄×C₈₉	—	2	2	no	—
173	C₂×C₄×C₈₉	—	2	4	no	—
174	C₂×C₄×C₈₉	—	2	2	no	—
175	C₂×C₄×C₈₉	—	2	2	no	—
176	C₂×C₄×C₈₉	—	2	2	no	—
177	C₂×C₄×C₈₉	—	4	2	no	—
178	C₂×C₄×C₈₉	—	4	2	no	—
179	C₂×C₄×C₈₉	—	4	2	no	—
180	C₂×C₄×C₈₉	—	4	2	no	—
181	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
182	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
188	C₈×C₈₉	—	2	2	no	—
189	C₈×C₈₉	—	2	2	no	—
190	C₈×C₈₉	—	4	2	no	—
191	C₈×C₈₉	—	4	2	no	—
192	C₈×C₈₉	C₄×D₄	1	2	yes	—
193	C₈×C₈₉	C₄×D₄	1	2	yes	—
194	C₈×C₈₉	#121	1	4	yes	—
195	C₂²×C₈₉	—	2	2	no	—
196	C₂²×C₈₉	—	2	4	no	—
197	C₂²×C₈₉	—	2	2	no	—
198	C₂²×C₈₉	—	4	2	no	—
199	C₂²×C₈₉	—	4	2	no	—
200	C₂²×C₈₉	—	4	4	no	—
201	C₂²×C₈₉	—	4	2	no	—
202	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
203	C₂²×C₈₉	#525	1	1	yes	characteristic
204	C₂²×C₈₉	#529	1	1	yes	characteristic
205	C₄×C₈₉	—	2	2	no	—
206	C₄×C₈₉	—	4	2	no	—
207	C₄×C₈₉	—	4	2	no	—
208	C₄×C₈₉	—	4	4	no	—
209	C₄×C₈₉	—	4	2	no	—
210	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
211	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
212	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
213	C₄×C₈₉	#532	1	1	yes	characteristic
214	#21550	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂×C₈₉	—	2	1	no	—
216	C₂×C₈₉	—	2	1	no	—
217	C₂×C₈₉	—	4	2	no	—
218	C₂×C₈₉	—	8	2	no	—
219	C₂×C₈₉	C₄×#121	1	1	yes	characteristic
220	C₂×C₈₉	#2955	1	2	yes	—
221	#3054	C₂×C₈₉	1	1	yes	characteristic
222	C₂×#444	C₂×C₈₉	1	1	yes	characteristic, complemented
223	#2929	C₂×C₈₉	1	2	yes	complemented
224	C₂×#405	C₂×C₈₉	1	1	yes	characteristic, complemented
225	#1974	C₂×C₈₉	1	1	yes	characteristic, complemented
226	#1945	C₂×C₈₉	1	1	yes	characteristic, complemented
227	#1937	C₂×C₈₉	1	2	yes	complemented
228	#1897	C₂×C₈₉	1	2	yes	complemented
229	#1811	C₂×C₈₉	1	1	yes	characteristic, complemented
230	#1773	C₂×C₈₉	1	1	yes	characteristic, complemented
231	#1765	C₂×C₈₉	1	2	yes	complemented
232	C₈₉	#21550	1	1	yes	characteristic, direct product factor, Sylow
233	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic
234	C₂×#131	C₂²×C₈₉	1	2	yes	—
235	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
236	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
237	#525	C₂²×C₈₉	1	2	yes	—
238	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
239	#470	C₄×C₈₉	1	2	yes	complemented
240	#469	C₄×C₈₉	1	2	yes	complemented
241	#468	C₄×C₈₉	1	4	yes	complemented
242	#444	—	2	4	no	—
243	#435	—	2	4	no	—
244	C₈×D₄	—	2	4	no	—
245	C₂×#108	C₂²×C₈₉	1	1	yes	characteristic
246	C₂×#108	C₂²×C₈₉	1	1	yes	characteristic
247	#427	C₂²×C₈₉	1	1	yes	characteristic
248	#424	C₂²×C₈₉	1	2	yes	—
249	C₂×#104	C₂²×C₈₉	1	2	yes	—
250	C₂×#104	C₂²×C₈₉	1	2	yes	—
251	#416	C₂²×C₈₉	1	2	yes	—
252	#408	C₂²×C₈₉	1	2	yes	—
253	#407	C₂²×C₈₉	1	2	yes	—
254	#405	—	2	4	no	—
255	#405	C₂²×C₈₉	1	2	yes	—
256	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
257	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
258	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
259	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
260	#341	C₂²×C₈₉	1	2	yes	—
261	#339	C₂²×C₈₉	1	2	yes	—
262	#339	C₂²×C₈₉	1	2	yes	—
263	C₂×#41	C₂³×C₈₉	1	2	yes	—
264	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
265	#135	—	2	2	no	—
266	#135	—	2	2	no	—
267	C₂×Q₁₆	C₂×C₄×C₈₉	1	1	yes	characteristic
268	C₂×SD₁₆	C₂×C₄×C₈₉	1	2	yes	—
269	C₂×D₈	C₂×C₄×C₈₉	1	1	yes	characteristic
270	#131	—	2	4	no	—
271	#131	—	2	4	no	—
272	C₂×M₁₆	—	2	2	no	—
273	C₂×M₁₆	—	2	2	no	—
274	C₂×M₁₆	—	2	2	no	—
275	C₂×M₁₆	C₂×C₄×C₈₉	1	2	yes	—
276	C₂×M₁₆	C₂×C₄×C₈₉	1	2	yes	—
277	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
278	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
279	C₂²×C₈	—	2	2	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	—	2	2	no	—
282	C₂²×C₈	D₄×C₈₉	1	4	yes	—
283	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
284	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
285	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
287	#123	—	2	2	no	—
288	C₂²⋊Q₈	C₂×C₄×C₈₉	1	4	yes	—
289	#121	C₂×C₄×C₈₉	1	4	yes	—
290	#120	—	2	2	no	—
291	C₄×D₄	—	2	4	no	—
292	#117	—	2	2	no	—
293	#117	—	2	2	no	—
294	#117	C₂³×C₈₉	1	2	yes	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
298	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
299	#108	—	2	2	no	—
300	#108	—	2	2	no	—
301	#107	C₂×C₄×C₈₉	1	2	yes	—
302	#106	C₂×C₄×C₈₉	1	2	yes	—
303	C₄⋊C₈	—	2	4	no	—
304	#104	—	2	4	no	—
305	#104	—	2	4	no	—
306	#103	C₂×C₄×C₈₉	1	4	yes	—
307	#102	C₂×C₄×C₈₉	1	4	yes	—
308	C₂²⋊C₈	—	2	4	no	—
309	C₂²⋊C₈	—	2	4	no	—
310	#97	—	2	2	no	—
311	#97	—	2	2	no	—
312	#97	D₄×C₈₉	1	4	yes	complemented
313	C₄×C₈	—	2	2	no	—
314	C₄×C₈	—	2	2	no	—
315	C₄×C₈	—	2	2	no	—
316	C₂⁴	#41×C₈₉	1	1	yes	characteristic
317	#41	—	2	2	no	—
318	#41	—	2	2	no	—
319	#41	—	2	2	no	—
320	#41	—	2	2	no	—
321	C₂×Q₈	C₂²×C₄×C₈₉	1	2	yes	—
322	C₂×D₄	—	2	4	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	C₂²×C₄×C₈₉	1	2	yes	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
334	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
335	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
336	Q₁₆	—	2	2	no	—
337	SD₁₆	—	2	4	no	—
338	D₈	—	2	2	no	—
339	M₁₆	—	2	4	no	—
340	M₁₆	—	2	4	no	—
341	M₁₆	—	2	2	no	—
342	M₁₆	—	2	2	no	—
343	M₁₆	—	2	2	no	—
344	M₁₆	—	2	2	no	—
345	M₁₆	—	4	4	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	8	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	4	4	no	—
354	C₂×C₈	C₂²×C₄×C₈₉	1	2	yes	—
355	C₂×C₈	C₂²×C₄×C₈₉	1	1	yes	characteristic
356	C₂×C₈	C₂²×C₄×C₈₉	1	1	yes	characteristic
357	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
358	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
359	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
360	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
361	C₂×C₈	#41×C₈₉	1	2	yes	—
362	C₂×C₈	#41×C₈₉	1	2	yes	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	C₂²×C₄×C₈₉	1	4	yes	—
366	C₂²⋊C₄	—	2	4	no	—
367	C₂²⋊C₄	—	2	4	no	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	1	no	—
373	C₄²	C₂×D₄×C₈₉	1	2	yes	—
374	C₄²	#41×C₈₉	1	2	yes	—
375	C₂³	—	2	1	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	2	2	no	—
378	C₂³	—	4	2	no	—
379	C₂³	C₄×D₄×C₈₉	1	2	yes	—
380	C₂³	C₂×#41×C₈₉	1	1	yes	characteristic
381	Q₈	—	2	2	no	—
382	Q₈	—	2	2	no	—
383	D₄	—	2	2	no	—
384	D₄	—	2	2	no	—
385	D₄	—	4	8	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	C₄×D₄×C₈₉	1	2	yes	—
403	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
404	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
405	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
406	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
407	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
408	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	—	2	2	no	—
411	C₈	—	4	2	no	—
412	C₈	—	4	2	no	—
413	C₈	C₄×D₄×C₈₉	1	2	yes	—
414	C₈	C₄×D₄×C₈₉	1	2	yes	—
415	C₈	#121×C₈₉	1	4	yes	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	4	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	4	4	no	—
423	C₂²	C₂×C₄×D₄×C₈₉	1	1	yes	characteristic
424	C₂²	#525×C₈₉	1	1	yes	characteristic
425	C₂²	#529×C₈₉	1	1	yes	characteristic
426	C₄	—	2	2	no	—
427	C₄	—	4	2	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	4	no	—
431	C₄	C₂×C₄×D₄×C₈₉	1	1	yes	characteristic
432	C₄	C₄×#41×C₈₉	1	1	yes	characteristic
433	C₄	C₂×#121×C₈₉	1	1	yes	characteristic
434	C₄	#532×C₈₉	1	1	yes	characteristic
435	C₂	—	2	1	no	—
436	C₂	—	2	1	no	—
437	C₂	—	4	2	no	—
438	C₂	—	8	2	no	—
439	C₂	C₄×#121×C₈₉	1	1	yes	characteristic
440	C₂	C₈₉×#2955	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₈₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₈₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₈₉×#3054	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈₉ ◁ C₂³×C₈×C₈₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×#444×C₈₉	C₂	semidirect
3. C₈₉×#2929	C₂	semidirect
4. C₂×#405×C₈₉	C₂	semidirect
5. C₈₉×#1974	C₂	semidirect
6. C₈₉×#1945	C₂	semidirect
7. C₈₉×#1937	C₂	semidirect
8. C₈₉×#1897	C₂	semidirect
9. C₈₉×#1811	C₂	semidirect
10. C₈₉×#1773	C₂	semidirect
11. C₈₉×#1765	C₂	semidirect
18. #470×C₈₉	C₄	semidirect
19. #469×C₈₉	C₄	semidirect
20. #468×C₈₉	C₄	semidirect
91. #97×C₈₉	D₄	semidirect
214. #21550	C₈₉	direct (N × H)
222. C₂×#444	C₂×C₈₉	semidirect
223. #2929	C₂×C₈₉	semidirect
224. C₂×#405	C₂×C₈₉	semidirect
225. #1974	C₂×C₈₉	semidirect
226. #1945	C₂×C₈₉	semidirect
227. #1937	C₂×C₈₉	semidirect
228. #1897	C₂×C₈₉	semidirect
229. #1811	C₂×C₈₉	semidirect
230. #1773	C₂×C₈₉	semidirect
231. #1765	C₂×C₈₉	semidirect
232. C₈₉	#21550	direct (N × H)
239. #470	C₄×C₈₉	semidirect
240. #469	C₄×C₈₉	semidirect
241. #468	C₄×C₈₉	semidirect
312. #97	D₄×C₈₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₈₉×#3054	2
C₂×#444×C₈₉	2
C₈₉×#2929	2
C₂×#405×C₈₉	2
C₈₉×#1974	2
C₈₉×#1945	2
C₈₉×#1937	2
C₈₉×#1897	2
C₈₉×#1811	2
C₈₉×#1773	2
C₈₉×#1765	2
#21550	89

Subgroups — C89×#21550 #36399398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#21550 #36399398